Greenland, the world's biggest island, has been part of Denmark for 600 years although its 57,000 people now govern their own domestic affairs. The island's government led by Prime Minister Mute Egede aims for eventual independence.

"We fully recognise that Greenland has its own ambitions. If they materialise, Greenland will become independent, though hardly with an ambition to become a federal state in the United States," Danish foreign minister Lars Lokke Rasmussen said.

He told reporters the United States' heightened security concerns in the Arctic were legitimate following increased Russian and Chinese activity in the region.

"I don't think that we're in a foreign policy crisis," he said. "We are open to a dialogue with the Americans on how we can possibly cooperate even more closely than we do to ensure that the American ambitions are fulfilled."

European allies jolted

Still, although Denmark itself played down the seriousness of Trump's threat to its territory, the returning president's openly stated ambition to expand U.S. borders has jolted European allies less than two weeks before he takes office.

France's foreign minister, Jean-Noel Barrot, said Europe would not let other nations attack its sovereign borders, although he did not believe the U.S. would invade.

A German government spokesperson said Berlin stood by the principle that borders must not be changed by force. A spokesperson for the European Commission said the sovereignty of EU member states had to be respected.

Strained relations

Greenland's relations with Denmark have lately been strained by allegations of colonial-era mistreatment of Greenlanders. Egede has said the island is not for sale, while in his New Year speech he stepped up his push for independence. Denmark says the territory's fate can be decided only by Greenlanders.

Danish Prime Minister Mette Frederiksen said on Tuesday she could not imagine Trump's ambitions would lead to U.S. military intervention in Greenland. Denmark's military capabilities there are limited to four inspection vessels, a Challenger surveillance plane and dog sled patrols.

Trade war worries

Responding to Trump's threat of tariffs against Denmark, Frederiksen said she did not think a trade war with the United States was a good way forward. Denmark is home to Novo Nordisk, Europe's most valuable company, which makes weight-loss drug Wegovy that has become hugely popular in the United States.

Trump already raised the issue of the U.S. taking over Greenland during his first presidency, but his latest remarks still left many Danes baffled.

"I find it extremely ridiculous," said Jeppe Finne Sorenson, a data engineer in the Danish capital. "We have an alliance, we're allies. So this doesn't really respect that."